Is the common parameterization of supersaturation with respect to ice as a linear function of temperature valid?

Supersaturation with respect to ice (Si) determines the strength of nonequilibrium fractionation during vapor deposition onto ice or snow, and therefore influences the isotopic composition, especially the deuterium excess, of vapor and precipitation in cold environments. Historically, most general circulation models would apply saturation adjustment for the formation of both liquid and ice clouds, which means that no supersaturation was allowed to occur. To calculate nonequilibrium fractionation during deposition, Si in these models therefore had to be parameterized. Commonly this was done by assuming a linear dependence on temperature in the form of Si = a + b*T. However, in nature the relation between Si and T is likely more complex than a linear function. Moreover, an Si function tuned for present-day climate might not represent past climate conditions (e.g. during the last glacial maximum) correctly. The recently developed isotope-enabled Community Atmosphere Model version 5 (iCAM5) explicitly allows ice supersaturation and thus provides a physical link to the strength of nonequilibrium fractionation during deposition without the need for tuning. Here we use this model to evaluate the commonly used parameterization of Si as a linear function of temperature. We present results for the present-day climate as well as the last glacial maximum. While the two Si versions lead to similar deuterium excess values in general, considerable differences can occur for individual events. Additionally, our results show that by using the explicitly modeled Si, water isotopes are more closely tied to the model physics and are therefore more useful as observational constraints.